Optical waveguide and arrayed waveguide grating

ABSTRACT

A technique that does not increase the circuit size, does not make the circuit design and manufacturing difficult, and can reduce insertion loss when light enters from a slab waveguide toward an arrayed waveguide or when the light enters from the arrayed waveguide toward the slab waveguide. An optical waveguide provided with a slab waveguide in which a grating is formed therein at a distance from an end, and an arrayed waveguide whose end is connected to an end of the slab waveguide at a position where a constructive interference portion of a self-image of the grating is formed. An arrayed waveguide grating provided with a first input/output waveguide, the above-mentioned optical waveguide where an end of the slab waveguide on the opposite side of the arrayed waveguide is connected to an end of the first input/output waveguide, a second slab waveguide connected to an end of the arrayed waveguide on the opposite side of the slab waveguide, and a second input/output waveguide connected to an end of the second slab waveguide on the opposite side of the arrayed waveguide.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a continuation of U.S. patent applicationSer. No. 13/698,573, filed Nov. 16, 2012, which is a national stageentry of PCT Patent Application No. PCT/JP2011/060699, filed May 10,2011, which claims priority to Japanese Patent Application No.2010-251223, filed Nov. 9, 2010, and to Japanese Patent Application No.2010-121904, filed May 27, 2010, the contents of each of which arehereby incorporated by reference in their entireties.

BACKGROUND OF THE DISCLOSURE

1. Field of the Disclosure

The present disclosure relates to an optical waveguide and an arrayedwaveguide grating, which can reduce insertion loss when light entersfrom a slab waveguide toward an arrayed waveguide or when the lightenters from the arrayed waveguide toward the slab waveguide.

2. Description of Related Art

In a DWDM (Dense Wavelength Division Multiplexing)multiplexer/demultiplexer, an M×N star coupler, a 1×N splitter, and soon, Patent Documents 1 to 6 disclose such a connection structure betweena slab waveguide and an arrayed waveguide that when light enters from aslab waveguide toward an arrayed waveguide, the light does not radiatein a clad layer as a radiation mode between the arrayed waveguidesadjacent to each other.

In the Patent Documents 1 to 4, a transition region where the refractiveindex of the waveguide gradually changes from the slab waveguide towardthe arrayed waveguide is disposed. In the Patent Document 5, a slopeportion is disposed between the slab waveguide and the arrayedwaveguide. In the Patent Document 6, a core layer and a plurality ofisland-shaped regions are arranged in the slab waveguide. The refractiveindex of the island-shaped region is smaller than the refractive indexof the core layer. The island-shaped regions face a clad layer providedbetween the adjacent arrayed waveguides. The width of the island-shapedregion in a direction substantially vertical to a light propagationdirection becomes narrower from the slab waveguide toward the arrayedwaveguide. Light passing through the core layer provided between theisland-shaped regions adjacent to each other propagates toward thearrayed waveguide without changing the propagation direction. Lightpassing through the island-shaped region changes the propagationdirection due to a tapered shape of the island-shaped region andpropagates toward the arrayed waveguide. The tapered shape and theposition of the island-shaped region are optimized, whereby the light isconcentrated on the arrayed waveguide and propagates in the arrayedwaveguide as a propagation mode.

PATENT DOCUMENTS

-   [Patent Document 1] U.S. Pat. No. 5,745,618-   [Patent Document 2] U.S. Pat. No. 7,006,729-   [Patent Document 3] U.S. Pat. No. 6,892,004-   [Patent Document 4] JP 2008-293020 A-   [Patent Document 5] JP 2001-159718 A-   [Patent Document 6] JP 2003-14962 A

In the Patent Documents 1 to 4, a large circuit size is required sincethe transition region is disposed. In the Patent Document 5, circuitmanufacturing is difficult since the slope portion is disposed. In thePatent Document 6, circuit designing is difficult since the taperedshape and the position of the island-shaped region are required to beoptimized.

Thus, in order to solve the above problems, the present disclosure hasthe purpose of providing an optical waveguide and an arrayed waveguidegrating, which do not increase the circuit size, do not make the circuitdesign and manufacturing difficult, and can reduce insertion loss whenlight enters from a slab waveguide toward an arrayed waveguide or whenthe light enters from the arrayed waveguide toward the slab waveguide.

SUMMARY OF THE DISCLOSURE

In order to achieve the above object, a grating is formed in the slabwaveguide, and an end of the arrayed waveguide is disposed at a positionwhere a constructive interference portion of a self-image of the gratingis formed.

Specifically, the present disclosure provides an optical waveguide whichis provided with a slab waveguide in which a grating is formed thereinat a distance from an end and an arrayed waveguide whose end isconnected to an end of the slab waveguide at a position where aconstructive interference portion of a self-image of the grating isformed.

According to the above constitution, due to Talbot effect, theself-image of the grating is formed according to wavelength of light anda period of the grating formed in the slab waveguide. The end of thearrayed waveguide is disposed at the position where the constructiveinterference portion of the self-image of the grating is formed, so thatwhen light enters from the slab waveguide toward the arrayed waveguide,the light is concentrated on the arrayed waveguide and propagates in thearrayed waveguide as a propagation mode. The size of an opticalwaveguide is not increased, the design and manufacturing is not madedifficult, and insertion loss can be reduced when the light enters fromthe slab waveguide toward the arrayed waveguide or when the light entersfrom the arrayed waveguide toward the slab waveguide.

Further, the present disclosure provides an optical waveguide in whichthe grating is a phase grating.

According to the above constitution, the incident light is diffracteddue to a phase difference given to incident light, and therefore, lossof the incident light can be reduced.

Furthermore, the present disclosure provides an optical waveguide inwhich the phase difference given to the incident light by the phasegrating is approximately 90 degrees.

According to the above constitution, the self-image of the phase gratingis clearly formed.

Furthermore, the present disclosure provides an optical waveguide inwhich the phase difference given to the incident light by the phasegrating is approximately 180 degrees.

According to the above constitution, the self-image of the phase gratingis clearly formed.

Furthermore, the present disclosure provides an optical waveguide inwhich the phase grating is provided with refractive index differenceregions which are disposed in the slab waveguide at a distance in adirection substantially vertical to a light propagation direction andhave a refractive index different from the refractive indices of otherregions in the slab waveguide.

According to the above constitution, the phase grating can be easilyformed in the slab waveguide.

Furthermore, the present disclosure provides an optical waveguide inwhich the refractive index difference regions adjacent to each other areconnected by a region having a refractive index equal to the refractiveindex of the refractive index difference region, and the refractiveindex difference regions are integral with each other across the entirephase grating.

According to the above constitution, the phase grating can be easilyformed in the slab waveguide.

Furthermore, the present disclosure provides an optical waveguide whichis provided with one or more first input/output waveguide(s), an opticalwaveguide where an end of the slab waveguide on an opposite side of thearrayed waveguide is connected to an end of the first input/outputwaveguide, a second slab waveguide connected to an end of the arrayedwaveguide on an opposite side of the slab waveguide, and one or moresecond input/output waveguide(s) connected to an end of the second slabwaveguide on the opposite side of the arrayed waveguide.

According to the above constitution, the size of the arrayed waveguidegrating is not increased, the design and manufacturing is not madedifficult, and the insertion loss can be reduced when light enters fromthe slab waveguide toward the arrayed waveguide or when the light entersfrom the arrayed waveguide toward the slab waveguide.

Furthermore, the present disclosure provides an arrayed waveguidegrating which is provided with two or more first input/outputwaveguides, a first slab waveguide connected to an end of the firstinput/output waveguides, an arrayed waveguide connected to an end of thefirst slab waveguide on an opposite side of the first input/outputwaveguides, a second slab waveguide connected to an end of the arrayedwaveguide on an opposite side of the first slab waveguide, and one ormore second input/output waveguide(s) connected to an end of the secondslab waveguide on an opposite side of the arrayed waveguide, wherein inthe first slab waveguide, a grating is formed therein at a distance froman end, and an end of the arrayed waveguide is connected to a positiondeviated from a position where a constructive interference portion of aself-image of the grating is formed so that a light intensitydistribution from the first input/output waveguides is substantiallyuniform when light enters from the second input/output waveguide towardthe first input/output waveguides.

According to the above constitution, loss in two or more of the firstinput/output waveguides can be uniformed in a demultiplexer throughwhich light enters from the second input/output waveguide toward thefirst input/output waveguide or a multiplexer through which light entersfrom the first input/output waveguide toward the second input/outputwaveguide.

Furthermore, the present disclosure provides an arrayed waveguidegrating in which the grating is a phase grating.

According to the above constitution, the incident light is diffracteddue to a phase difference given to the incident light, and therefore,loss of the incident light can be reduced.

Furthermore, the present disclosure provides an arrayed waveguidegrating in which the phase difference given to the incident light by thephase grating is approximately 90 degrees.

According to the above constitution, the self-image of the phase gratingis clearly formed.

Furthermore, the present disclosure provides an arrayed waveguidegrating in which the phase difference given to the incident light by thephase grating is approximately 180 degrees.

According to the above constitution, the self-image of the phase gratingis clearly formed.

Furthermore, the present disclosure provides an arrayed waveguidegrating in which the phase grating is provided with refractive indexdifference regions which are disposed in the slab waveguide at adistance in a direction substantially vertical to a light propagationdirection and have a refractive index different from the refractiveindices of other regions in the slab waveguide.

According to the above constitution, the phase grating can be easilyformed in the slab waveguide.

Furthermore, the present disclosure provides an arrayed waveguidegrating in which the refractive index difference regions adjacent toeach other are connected by a region having a refractive index equal tothe refractive index of the refractive index difference regions, and therefractive index difference regions are integral with each other acrossthe entire phase grating.

According to the above constitution, the phase grating can be easilyformed in the slab waveguide.

EFFECTS OF THE DISCLOSURE

The present disclosure can provide an optical waveguide and an arrayedwaveguide grating, which do not increase the circuit size, do not makethe circuit design and manufacturing difficult, and can reduce insertionloss when light enters from a slab waveguide toward an arrayed waveguideor when the light enters from the arrayed waveguide toward the slabwaveguide.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a view showing a phenomenon of Talbot effect.

FIG. 2 is a view showing the phenomenon of the Talbot effect.

FIG. 3 is a view showing calculation results of the Talbot effect.

FIG. 4 is a view showing calculation results of the Talbot effect.

FIG. 5 is a view showing calculation results of the Talbot effect.

FIGS. 6A, 6B and 6C are views showing a positional relationship betweena phase grating of a slab waveguide and an incident end of an arrayedwaveguide.

FIG. 7 is a view showing the calculation results of the Talbot effect.

FIG. 8 is a view showing a positional relationship between the phasegrating of the slab waveguide and the incident end of the arrayedwaveguide.

FIG. 9 is a view showing a structure of an optical waveguide.

FIG. 10 is a view showing a method of manufacturing the opticalwaveguide using ultraviolet irradiation.

FIG. 11 is a view showing the method of manufacturing the opticalwaveguide using ultraviolet irradiation.

FIGS. 12A, 12B, 12C and 12D are views showing a structure of the opticalwaveguide.

FIGS. 13A and 13B are views showing a structure of the opticalwaveguide.

FIGS. 14A, 14B and 14C are views showing a structure of the opticalwaveguide.

FIG. 15 is a view showing loss distributions between output channels.

FIG. 16 is a view showing a relationship between an interference regionlength and a minimum loss.

FIG. 17 is a view showing a relationship between the interference regionlength and loss variation between the output channels.

DETAILED DESCRIPTION OF THE DISCLOSURE

Embodiments of the present disclosure will be described with referenceto the accompanying drawings. The embodiments to be describedhereinafter are examples of the present disclosure, and the presentdisclosure is not limited to the following embodiments. Componentsdenoted by the same reference numerals in the description and thedrawings mutually represent the same components.

Embodiment 1

In an Embodiment 1, first, a phenomenon and calculation results ofTalbot effect will be described. Next, an optical waveguide which canreduce insertion loss when light enters from a slab waveguide toward anarrayed waveguide or when the light enters from the arrayed waveguidetoward the slab waveguide will be described based on the phenomenon andthe calculation results of the Talbot effect.

The Talbot effect means that diffracted lights interfere with each otherwhen light enters a grating, whereby a light intensity distributionsimilar to a pattern of the grating is realized as a self-image of thegrating at a position apart from the grating with a distance specifiedaccording to the wavelength of the light and a period of the grating,and the Talbot effect is applied to a Talbot interferometer.

FIGS. 1 and 2 are views showing the phenomenon of the Talbot effect.Gratings GP1 and GP2 are phase gratings giving a phase difference toincident light, and a grating GA is an amplitude grating giving anintensity difference to the incident light. The phenomenon of the Talboteffect associated with the phase grating GP1 is shown in an upper halfof FIG. 1, the phenomenon of the Talbot effect associated with theamplitude grating GA is shown in a lower half of FIG. 1, and thephenomenon of the Talbot effect associated with the phase grating GP2 isshown in FIG. 2. Each period of the phase gratings GP1 and GP2 and theamplitude grating GA is d. The phase difference given to the incidentlight by the phase grating GP1 is 90°. The phase difference given to theincident light by the phase grating GP2 is 180°. The phase gratings GP1and GP2 and the amplitude grating GA are arranged at a position of z=0in an x-y plane (y axis is not shown in FIGS. 1 and 2) (in FIGS. 1 and2, as a matter of convenience, the phase gratings GP1 and GP2 and theamplitude grating GA are shown on the left side of the drawings relativeto the position of z=0). The wavelength of the incident light is λ. Theincident light enters as parallel light in the z-axis direction as shownby arrows at the left ends of FIGS. 1 and 2.

First, the phenomenon of the Talbot effect associated with the phasegrating GP1 will be described. When z=md²/(2λ), a light intensitydistribution formed immediately after the phase grating GP1 is uniformat the position of m=0 as shown by a sand portion, and light intensitydistributions similar to this light intensity distribution are shown atpositions of m=2, 4, 6, 8, . . . , 4n+2, 4n+4, . . . (n is an integer ofnot less than 0). Meanwhile, at positions of m=1, 3, 5, 7, . . . , 4n+1,4n+3, . . . , self-images SP1 of the phase grating GP1 are clearlyformed as shown by diagonal lines and white portions. Although theself-images SP1 of the phase grating GP1 are formed at positions otherthan the positions of m=1, 3, 5, 7, . . . , 4n+1, 4n+3, . . . , theself-images SP1 are not clearly formed, and a boundary between aconstructive interference portion and a destructive interference portionis not clear. The intensity period of the self-image SP1 of the phasegrating GP1 is d.

The self-images SP1 of the phase grating GP1 formed at the positions ofm=1, 5, . . . , 4n+1, . . . are shifted by d/2 in the x-axis directionin comparison with the self-images SP1 of the phase grating GP1 formedat the positions of m=3, 7, . . . , 4n+3, . . . .

Next, the phenomenon of the Talbot effect associated with the amplitudegrating GA will be described. When z=md²/(2λ), the light intensitydistribution formed immediately after the amplitude grating GA is shownat the position of m=0, and light intensity distributions similar tothis light intensity distribution are shown as self-images SA of theamplitude grating GA at the positions of m=2 and 4. Although theself-images SA of the amplitude grating GA are clearly formed at theposition of m=2, 4, 6, 8, . . . , 4n+2, 4n+4, . . . (n is an integer ofnot less than 0) as shown by diagonal lines and white portions, theself-images SA of the amplitude grating GA are not formed at thepositions of m=1, 3, 5, 7, . . . , 4n+1, 4n+3, . . . as shown by sandportions, and a uniform intensity distribution exists. Although theself-images SA of the amplitude grating GA are formed at positions otherthan the positions of m=2, 4, 6, 8, . . . , 4n+2, 4n+4, . . . , theself-images SA are not clearly formed, and the boundary between theconstructive interference portion and the destructive interferenceportion is not clear. The intensity period of the self-image SA of theamplitude grating GA is d.

The self-images SA of the amplitude grating GA formed at the positionsof m=2, 6, . . . , 4n+2, . . . are shifted by d/2 in the x-axisdirection in comparison with the self-images SA of the amplitude gratingGA formed at the positions of m=4, 8, . . . , 4n+4, . . . .

Next, the phenomenon of the Talbot effect associated with the phasegrating GP2 will be described. When z=md²/(8λ), the light intensitydistribution formed immediately after the phase grating GP2 is uniformat the position of m=0 as shown by a sand portion, and light intensitydistributions similar to this light intensity distribution are shown atthe positions of m=2, 4, 6, . . . , 2n, (n is an integer of not lessthan 0). Meanwhile, at the positions of m=1, 3, 5, 7, . . . , 2n+1, . .. , self-images SP2 of the phase grating GP2 are clearly formed as shownby diagonal lines and white portions. Although the self-images SP2 ofthe phase grating GP2 are formed at positions other than the positionsof m=1, 3, 5, 7, . . . , 2n+1, . . . , the self-images SP2 are notclearly formed, and the boundary between the constructive interferenceportion and the destructive interference portion is not clear. Theintensity period of the self-image SP2 of the phase grating GP2 is d/2.The self-image SP2 does not shift for each order.

The phase gratings GP1 and GP2 change the speed of light according tothe position of their x coordinate and give a phase difference toincident light. The amplitude grating GA changes absorption of lightaccording to the position of the x coordinate and gives an intensitydifference to the incident light. Accordingly, when the opticalwaveguide according to the present disclosure is applied to an arrayedwaveguide grating described in an Embodiment 4, the phase gratings GP1and GP2 are preferably used in order to reduce loss of light. Thus, inthe following description, the case of using the phase gratings GP1 andGP2 will be described in detail, and in the case of using the amplitudegrating GA, portions different from the case of using the phase gratingsGP1 and GP2 will be briefly described.

FIG. 3 is a view showing calculation results of the Talbot effect of thephase grating GP1. Although in FIG. 1, incident light is parallel light,the incident light in FIG. 3 is diffusion light in consideration thatthe light propagating in the slab waveguide is not parallel light butdiffusion light. The incident light enters as diffusion light in a rightdirection as shown by arrows at the left end of FIG. 3. FIG. 4 is a viewshowing calculation results of the Talbot effect of the phase gratingGP2. In FIG. 4, incident light is parallel light. The incident lightenters as parallel light in a right direction as shown by arrows at theleft end of FIG. 4. In FIGS. 3 and 4, the phase gratings GP1 and GP2 arearranged at the position of m=0.

Although the self-images SP1 of the phase grating GP1 are clearly formedat the positions of m=1, 3, 5, 7, . . . , 4n+1, 4n+3, . . . as shown bya clear black and white gradation, the self-images SP1 are not clearlyformed at the positions of m=2, 4, 6, 8, . . . , 4n+2, 4n+4, . . . asshown by an unclear black and white gradation. At positions other thanthe positions of m=1, 3, 5, 7, . . . , 4n+1, 4n+3, . . . , the closer tothe positions of m=1, 3, 5, 7, . . . , 4n+1, 4n+3, . . . , the moreclearly the self-image SP1 of the phase grating GP1 are formed, and thecloser to the positions of m=2, 4, 6, 8, . . . , 4n+2, 4n+4, . . . , theless clearly the self-image SP1 of the phase grating GP1 is formed. Thepositions of m=0, 1, 2, 3, . . . are not arranged at regular intervalsbecause the incident light is not parallel light but diffusion light.

When FIG. 3 is seen as a whole, the black and white gradation is spreadin the vertical direction of FIG. 3 as it progresses in the right sidedirection. When FIG. 3 is seen in detail, the black and white gradationdrastically changes near the positions of m=2, 4, 6, 8, . . . , 4n+2,4n+4, . . . . This result corresponds to the fact that in FIG. 1, theself-images SP1 of the phase grating GP1 formed at the positions of m=1,5, . . . , 4n+1, . . . are shifted by d/2 in the x-axis direction incomparison with the self-images SP1 of the phase grating GP1 formed atthe positions of m=3, 7, . . . , 4n+3, . . . . The self-images SP1 ofthe phase grating GP1 formed at the position of m=1, 3, 5, 7, . . . ,4n+1, 4n+3, . . . are more clearly formed as m becomes smaller. Althoughthe calculation results of FIG. 4 and a schematic drawing in FIG. 2 showsimilar tendencies, in FIG. 4 a peak having a period the same as theperiod of the phase grating GP2 is confirmed at the positions of m=2, 4,. . . . This is because while the simulation in FIG. 4 is calculationbased on a general optical circuit, when the phase grating GP2 is formedof a material having a small refractive index difference such as a corematerial and a clad material, the phase grating GP2 is elongated in alight propagation direction, light propagating in a portion having a lowrefractive index couples to a portion having a high refractive index asthe propagation distance becomes longer, and the intensity distributionoccurs at an end of the phase grating GP2.

FIG. 5 is a view showing calculation results of the Talbot effect on thephase grating GP giving various phase differences to incident light. InFIG. 5, the phase differences given to the incident light by the phasegrating GP are π/8, π/4, π/2, 3π/4, 7π/8, π, π/12, π/6, and π/3 at theleft end of the upper stage, the center of the upper stage, the rightend of the upper stage, the left end of the intermediate stage, thecenter of the intermediate stage, the right end of the intermediatestage, the left end of the lower stage, the center of the lower stage,and the right end of the lower stage, respectively. In FIG. 5, theincident light is parallel light, and the phase grating GP is disposedat the left end of each drawing. As long as the self-image SP of thephase grating GP can be clearly formed by the Talbot effect, the phasedifference given to the incident light by the phase grating GP may be aphase difference other than the above phase differences in FIG. 5.

Next, the optical waveguide, which can reduce the insertion loss whenlight enters from the slab waveguide toward the arrayed waveguide, orwhen the light enters from the arrayed waveguide toward the slabwaveguide, will be described based on the phenomenon and the calculationresults of the Talbot effect. FIGS. 6A, 6B and 6C are views showing apositional relationship between the phase grating GP1 or GP2 of a slabwaveguide 1 and an end of an arrayed waveguide 2. The respective leftsides of FIGS. 6A to 6C show the overall configuration of the opticalwaveguide, the respective right sides of FIGS. 6A and 6B show theself-image SP1 of the phase grating GP1, the right side of FIG. 6C showsthe self-image SP2 of the phase grating GP2, and in each of FIGS. 6A to6C, the left and right side views are aligned in the vertical directionof FIGS. 6A, 6B and 6C by alternate long and short dashed lines. InFIGS. 6A and 6B, the positional relationship between the phase gratingGP1 of the slab waveguide 1 and the end of the arrayed waveguide 2 isdifferent from each other.

The slab waveguide 1 is constituted of an incident region IN, the phasegrating GP1 or GP2, and an interference region IF. The incident regionIN is disposed on the incident side of the slab waveguide 1, andincident light propagates in the incident region IN. The phase gratingGP1 or GP2 is provided in the slab waveguide 1 and disposed between theincident region IN and the interference region IF, and formed from aregion shown by diagonal lines and a region shown by a white portion,which have different refractive indices. The refractive index of theregion shown by the diagonal lines may be larger or smaller than therefractive index of the region shown by the white portion. Incidentlight propagates in the region with a large refractive index at lowspeed and propagates in the region with a small refractive index at highspeed. The phase grating GP1 or GP2 changes the speed of light accordingto the position in the vertical direction of FIGS. 6A, 6B and 6C andgives a phase difference to the incident light. The interference regionIF is disposed at an end of the slab waveguide 1 on the arrayedwaveguide 2 side, and diffraction light is propagated in theinterference region IF.

The arrayed waveguide 2 is connected to the interference region IF ofthe slab waveguide 1 at a constructive interference portion shown by thewhite portion of the self-image SP1 of the phase grating GP1 or theself-image SP2 of the phase grating GP2. Namely, since the diffractionlight is intensively distributed in the constructive interferenceportion shown by the white portion of the self-image SP1 of the phasegrating GP1 or the self-image SP2 of the phase grating GP2, thediffraction light propagates in the arrayed waveguide 2 as a propagationmode. Since the diffraction light is hardly distributed in a destructiveinterference portion shown by the diagonal lines of the self-image SP1of the phase grating GP1 or the self-image SP2 of the phase grating GP2,the diffraction light does not radiate in the clad layer as a radiationmode. In FIGS. 6A, 6B and 6C, a plurality of the array waveguides 2 areconnected; however, only one waveguide may be connected.

In FIG. 6A, at the position corresponding to the region shown by thediagonal lines of the phase grating GP1, the constructive interferenceportion shown by the white portion of the self-image SP1 of the phasegrating GP1 is formed, and the end of the arrayed waveguide 2 isconnected. In FIG. 6B, at the position corresponding to the region shownby the white portion of the phase grating GP1, the constructiveinterference portion shown by the white portion of the self-image SP1 ofthe phase grating GP1 is formed, and the end of the arrayed waveguide 2is connected. The different positional relationships thus exist as thepositional relationship between the phase grating GP1 of the slabwaveguide 1 and the end of the arrayed waveguide 2, and this resultcorresponds to the fact that, as shown in FIG. 1, the self-images SP1 ofthe phase grating GP1 formed at the positions of m=1, 5, . . . , 4n+1, .. . are shifted by d/2 in the x-axis direction in comparison with theself-images SP1 of the phase grating GP1 formed at the positions of m=3,7, . . . , 4n+3, . . . . In FIG. 6C, at a position advanced, in adirection substantially parallel to the light propagation direction,from the regions shown by the diagonal lines and the white portion ofthe phase grating GP2, the constructive interference portion shown bythe white portion of the self-image SP2 of the phase grating GP2 isformed, and the end of the arrayed waveguide 2 is connected. Althoughthe period of the phase grating GP1 is the same as the period of thearrayed waveguide 2 in FIGS. 6A and 6B, the period of the phase gratingGP2 is twice the period of the arrayed waveguide 2 in FIG. 6C.

Accordingly, when the period of the arrayed waveguide 2 is the same, thewidth in the direction substantially vertical to the light propagationdirection of the region with a small refractive index of the phasegrating GP2 of FIG. 6C is twice the width in the direction substantiallyvertical to the light propagation direction of the region with a smallrefractive index of the phase grating GP1 of FIGS. 6A and 6B. A lightpropagation direction width L1 of the phase grating GP2 is a lengthcorresponding to the phase difference π, and the light propagationdirection width L1 of the phase grating GP1 is a length corresponding tothe phase difference π/2; therefore, the width in the directionsubstantially parallel to the light propagation direction of the regionwith a small refractive index of the phase grating GP2 is twice thewidth in the direction substantially parallel to the light propagationdirection of the region with a small refractive index of the phasegrating GP1. When the region with a small refractive index thusincreases, light radiation loss increases when light propagates in theregion with a small refractive index.

In the phase grating GP2, a value obtained by dividing the width of theregion with a large refractive index in the direction substantiallyvertical to the light propagation direction by the period of the phasegrating GP2 in the direction substantially vertical to the lightpropagation direction is defined as duty ratio. FIG. 7 is a view showingthe calculation results of the Talbot effect of the phase grating GP2with various duty ratios. The duty ratios of the phase grating GP2 atthe left end, the center, and the right end of FIG. 7 are 0.75, 0.5, and0.25, respectively. In FIG. 7, incident light is parallel light, and thephase grating GP2 is disposed at the left end of each drawing. As theduty ratio becomes larger, the peak can be clearly formed at thepositions of m=2, 4, . . . . Accordingly, when the arrayed waveguide 2is disposed at the peak position, the period of the phase grating GP2and the period of the arrayed waveguide 2 are the same as each other,and the light radiation loss can be suppressed when light propagates inthe region with a small refractive index.

As described above, due to the Talbot effect, the self-image SP1, SP2,or SA of the grating GP1, GP2, or GA is formed according to thewavelength λ of the incident light and the period of the grating GP1,GP2 or GA formed in the slab waveguide 1. The end of the arrayedwaveguide 2 is disposed at the position where the constructiveinterference portion of the self-image SP1, SP2, or SA of the gratingGP1, GP2 or GA is formed, whereby the light is concentrated on thearrayed waveguide 2 and propagates as a propagation mode when lightenters from the slab waveguide 1 toward the arrayed waveguide 2.Accordingly, when the light enters from the slab waveguide 1 to thearrayed waveguide 2, the insertion loss can be reduced. Due toreciprocity of light, this also applies to the case where the lightenters from the arrayed waveguide 2 toward the slab waveguide 1. Whenthe arrayed waveguide 2 is branched near the boundary with the slabwaveguide 1, each end of the branched arrayed waveguides 2 is disposedat the position where the constructive interference portion is formed.

Embodiment 2

In an Embodiment 2, a method of designing an optical waveguide will bedescribed. First, a method of setting a light propagation directionwidth L1 of phase gratings GP1 and GP2 will be described, next, a methodof setting a light propagation direction width L2 of an interferenceregion IF will be described, and finally, a method of setting a positionof an end of an arrayed waveguide 2 will be described.

In order to clearly form a self-image SP1 of the phase grating GP1 atthe end of the arrayed waveguide 2, the light propagation directionwidth L1 of the phase grating GP1 is set so that a phase differencegiven to light by the phase grating GP1 is preferably 80 to 100°, morepreferably 90°. In order to clearly form a self-image SP2 of the phasegrating GP2 at the end of the arrayed waveguide 2, the light propagationdirection width L1 of the phase grating GP2 is set so that a phasedifference given to light by the phase grating GP2 is preferably 170 to190°, more preferably 180°.

Wavelength of light in vacuum is represented by λ, a refractive index ofa region with a large refractive index is represented by n, therefractive index of a region with a small refractive index isrepresented by n−δn, and a relative refractive index difference betweenthe region with a large refractive index and the region with a smallrefractive index is represented by Δ=δn/n. A phase lead angle at thetime when light passes from a start end to a terminal end of the regionwith a large refractive index is L1÷(λ/n)×2π=2πnL1/λ. The phase leadangle at the time when light passes from a start end to a terminal endof the region with a small refractive index isL1÷(λ/(n−δn))×2π=2π(n−δn)L1/λ. The phase difference given to light bythe phase grating GP is 2πnL1/λ−2π(n−δn)L1/λ=2πδnL1/λ=2πnΔL1/λ. L1 ispreferably set to be λ/(4nΔ) so that the phase difference given to lightby the phase grating GP1 is 90°. For example, when λ=1.55 n=1.45, andΔ=0.75%, L1 is preferably set to be about 35 μm so that the phasedifference given to light by the phase grating GP1 is 90°. L1 ispreferably set to be λ/(2nΔ) so that the phase difference given to lightby the phase grating GP2 is 180°. For example, when λ=1.55 n=1.45, and4=0.75%, L1 is preferably set to be about 70 μm so that the phasedifference given to light by the phase grating GP2 is 180°.

In order to clearly form the self-image SP of the phase grating GP atthe end of the arrayed waveguide 2, the light propagation directionwidth L2 of the interference region IF is set based on the descriptionsof FIGS. 1 to 4.

When the wavelength of light in vacuum is represented by λ, and therefractive index of the interference region IF is represented by n beingequal to the above refractive index of the region with a largerefractive index, the wavelength in the interference region IF of lightis λ/n. Based on the description of FIG. 1, L2 is set to be md²/(2(λ/n))as an optimum design with respect to the phase grating GP1. For example,when d=10.0 μm, λ=1.55 μm, and n=1.45, L2 is set to be about 47 μm as anoptimum design when m=1. Based on the description of FIG. 2, L2 is setto be md²/(8(λ/n)) as an optimum design with respect to the phasegrating GP2. For example, when d=20.0 μm, λ=1.55 n=1.45, L2 is set to beabout 47 μm as an optimum design when m=1. Based on the description ofFIG. 3, the calculation result of the Talbot effect is obtained with dueconsideration of diffusion of light, and L2 is set as the optimumdesign.

After the light propagation direction width L2 of the interferenceregion IF is set based on the descriptions of FIGS. 1 to 4, aconstructive interference portion of the self-image SP of the phasegrating GP at the terminal end of the interference region IF is set asthe position of the end of the arrayed waveguide 2 based on thedescriptions of FIGS. 1 to 4. It is preferable that among the ends ofthe plurality of arrayed waveguides 2, the self-image SP of the phasegrating GP is clearly formed at not only the end of the center arrayedwaveguide 2 but also the ends of the arrayed waveguides 2 disposed atboth edges of the plurality of arrayed waveguides 2. Thus, thepositional relationship between the phase grating GP of the slabwaveguide 1 and the end of the arrayed waveguide 2 is preferably thepositional relationship shown in FIG. 8. Namely, it is preferable thatthe number of the regions with a large refractive index of the phasegrating GP is larger than the number of the arrayed waveguides 2.

In order to reduce the size of the optical waveguide as well as toclearly form the self-image SP or SA of the grating GP or GA, it ispreferable that m is set to be small so that the light propagationdirection width L2 of the interference region IF becomes short. Thegrating GP or GA may have any shape including a shape to be described inan Embodiment 3 as long as it has a function of diffracting light. As inthe above description, the present disclosure does not increase the sizeof the optical waveguide and does not make the design difficult. Whenthe present disclosure is not employed, the propagation loss between theslab waveguide 1 and the arrayed waveguide 2 is approximately 0.45 dB;however, when this disclosure is employed in the above designing method,the loss can be reduced to not more than 0.1 dB.

Embodiment 3

In the Embodiment 3, a method of manufacturing an optical waveguide willbe described. FIGS. 9 to 12D are views showing a structure of theoptical waveguide. The optical waveguide shown in FIGS. 9 to 11 and theoptical waveguide shown in FIGS. 12A, 12B, 12C and 12D are different inthe structure of a phase grating GP.

The phase grating GP shown in FIG. 9 is provided with refractive indexdifference regions 11. The refractive index difference regions 11 aredisposed in a slab waveguide 1 at a distance in a directionsubstantially vertical to a light propagation direction and have arefractive index different from the refractive index of a region shownby diagonal lines. Although the refractive index difference region 11has a rectangular shape in the optical waveguide shown in FIG. 9, therefractive index difference region 11 may have any shape.

The refractive index of the refractive index difference region 11 may belarger or smaller than the refractive index of the region shown bydiagonal lines. A region with a large refractive index and a region witha small refractive index are alternately arranged in the directionsubstantially vertical to the light propagation direction, whereby thephase grating GP can be easily formed.

The methods of manufacturing an optical waveguide shown in FIG. 9include a method using lithography and etching and a method usingultraviolet irradiation.

In the method using lithography and etching, first, SiO₂ fine particlesbecoming a lower clad layer and SiO₂—GeO₂ fine particles becoming a corelayer are deposited on a Si substrate by a flame hydrolysis depositionmethod, and are heated and melted to be transparent. Next, anunnecessary portion of the core layer is removed by lithography andetching to form an optical circuit pattern, and at the same time, anunnecessary portion of the core layer is removed from a portion becomingthe refractive index difference region 11. Finally, the SiO₂ fineparticles becoming an upper clad layer are deposited by the flamehydrolysis deposition method, and are heated and melted to betransparent, whereby the upper clad layer is formed, so that the portionbecoming the refractive index difference region 11 is filled with a cladmaterial. Since the portion becoming the refractive index differenceregion 11 is filled with the clad material, the refractive index of therefractive index difference region 11 is smaller than the refractiveindex of the region shown by diagonal lines. In the above case, therefractive index difference region 11 is formed in the formation processof the slab waveguide 1 and the arrayed waveguide 2, however, after theformation of the slab waveguide 1 and the arrayed waveguide 2, theportion becoming the refractive index difference region 11 may begrooved and filled with resin and so on having a refractive indexdifferent from the refractive index of the core layer, or the refractiveindex difference region 11 may be formed by an air space using onlygrooving.

The method using ultraviolet irradiation utilizes the phenomenon thatthe refractive index is increased by ultraviolet irradiation. In thefirst method, after the formation of the lower clad layer and the corelayer, or after the formation of the lower clad layer, the core layer,and the upper clad layer, a mask material is formed on the portionbecoming the refractive index difference region 11, and the refractiveindices of portions other than the portion becoming the refractive indexdifference region 11 are changed by ultraviolet irradiation, whereby therefractive index difference region 11 is formed. The refractive index ofthe refractive index difference region 11 is smaller than the refractiveindex of the region shown by diagonal lines. In the second method, afterthe formation of the lower clad layer and the core layer, or after theformation of the lower clad layer, the core layer, and the upper cladlayer, a mask material is formed on a portion other than the portionbecoming the refractive index difference region 11, and the refractiveindex of the portion becoming the refractive index difference region 11is changed by ultraviolet irradiation, whereby the refractive indexdifference region 11 is formed. The refractive index of the refractiveindex difference region 11 is larger than the refractive index of theregion shown by diagonal lines.

FIGS. 10 and 11 are views showing the method of manufacturing an opticalwaveguide shown in FIG. 9 using ultraviolet irradiation. In themanufacturing method shown in FIG. 10, as shown in STEP 1, the upperclad layer is formed after the core layer is removed from the portionbecoming the phase grating GP. Then, as shown in STEP 2, ultravioletirradiation is performed after the mask material is formed on theportion becoming the refractive index difference region 11 or theportion other than the portion becoming the refractive index differenceregion 11. In the manufacturing method shown in FIG. 11, as shown inSTEP 1, the upper clad layer is formed after the core layer is processedas shown in FIG. 9 at a portion becoming the phase grating GP. Then, asshown in STEP 2, ultraviolet irradiation is performed after the maskmaterial is formed on the portion becoming the refractive indexdifference region 11. The refractive index difference between therefractive index difference region 11 and the region shown by diagonallines further increases after the ultraviolet irradiation compared tobefore the irradiation.

The interference region IF may be provided with any material as long asit has a function of interfering light. For example, the interferenceregion IF may be provided with at least one of materials including acore material, a clad material, SiO₂—GeO₂ irradiated with ultravioletlight, resin, and air.

The methods of manufacturing an optical waveguide shown in FIGS. 12A to12D are similar to the method of manufacturing an optical waveguideshown in FIG. 9. In a case where an upper clad material, resin, and soon are used to fill the refractive index difference region to form therefractive index difference region, it may be difficult to uniformlyfill the refractive index difference region 11 with the upper cladmaterial, the resin, and so on when a periphery of the refractive indexdifference region 11 is surrounded by the region shown by diagonal linesas shown in FIG. 9. On the other hand, as shown in FIGS. 12A to 12D,when refractive index difference region 12 forming the phase grating GPis integral across the entire phase grating GP, it is easy that therefractive index difference region is uniformly filled with the upperclad material, the resin, and so on.

The phase grating GP shown in FIG. 12A is provided with the refractiveindex difference region 12 and convex regions 13 and 14. The refractiveindex difference region 12 is provided with regions having a large widthand regions having a small width in the direction substantially verticalto the light propagation direction, and is integral across the entirephase grating GP. The regions with a large width are arranged in theslab waveguide 1 at a distance in the direction substantially verticalto the light propagation direction, and have a refractive indexdifferent from the refractive index of the region shown by diagonallines. Each of the regions with a small width is held between the convexregions 13 and 14, has a refractive index equal to the refractive indexof the regions with a large width, and connects the regions with a largewidth adjacent thereto.

The refractive index of the refractive index difference region 12 may belarger or smaller than the refractive index of the portion shown bydiagonal lines. The region with a large refractive index and the regionwith a small refractive index are alternately arranged in the directionsubstantially vertical to the light propagation direction, whereby thephase grating GP can be easily formed.

Although the convex regions 13 and 14 are arranged in the opticalwaveguide shown in FIG. 12A, only the convex regions 13 may be disposedas in the optical waveguide shown in FIG. 12B, and only the convexregions 14 may be disposed as in the optical waveguide shown in FIG.12C. In the optical waveguide shown in FIG. 12A, the sum of the lightpropagation direction widths of the convex regions 13 and 14 is set toL1 shown in FIGS. 6A to 6C, in the optical waveguide shown in FIG. 12B,the light propagation direction width of the convex region 13 is set toL1 shown in FIGS. 6A to 6C, and in the optical waveguide shown in FIG.12C, the light propagation direction width of the convex region 14 isset to L1 shown in FIGS. 6A to 6C. In the optical waveguides shown inFIGS. 12A to 12C, although the convex regions 13 and 14 have arectangular shape, they may have any shape.

In the optical waveguide shown in FIGS. 12A and 12B, a concave regionbetween the convex regions 13 adjacent thereto in the directionsubstantially vertical to the light propagation direction may have anyshape. In the optical waveguide shown in FIGS. 12A and 12C, a concaveregion between the convex regions 14 adjacent thereto in the directionsubstantially vertical to the light propagation direction may also haveany shape. Moreover, a boundary surface of the incident region IN or theinterference region IF may also have any shape.

As a variation of the optical waveguide shown in FIG. 12A, as in theoptical waveguide shown in FIG. 13A, a boundary surface region BS may beformed on a boundary surface between the convex region 13 and therefractive index difference region 12, on a boundary surface between theconvex region 14 and the refractive index difference region 12, and on aboundary surface between the concave region and the refractive indexdifference region 12. The boundary surface region BS shown in FIG. 13Ahas a refractive index which is the same as the refractive index of acore material constituting the interference region IF or has arefractive index between the refractive index of the core materialconstituting the interference region IF and the refractive index of theclad material constituting the refractive index difference region 12.

As a variation of the optical waveguide shown in FIG. 12C, as in theoptical waveguide shown in FIG. 13B, the boundary surface region BS maybe formed on a boundary surface between the convex region 14 and therefractive index difference region 12, on a boundary surface between theincident region IN or the interference region IF and the refractiveindex difference region 12, and on a boundary surface between theconcave region and the refractive index difference region 12. Theboundary surface region BS shown in FIG. 13B has a refractive indexwhich is the same as the refractive index of the clad materialconstituting the refractive index difference region 12 or has arefractive index between the refractive index of the core materialconstituting the interference region IF and the refractive index of theclad material constituting the refractive index difference region 12.

As in the optical waveguide shown in FIGS. 13A and 13B, the boundarysurface region BS whose surface extends in a direction different fromdirections substantially parallel and substantially vertical to thelight propagation direction is formed on a boundary surface betweenregions with different refractive indices, whereby it is possible toprevent light from being reflected, and it is also possible to preventlight from being reflected toward an input/output waveguide connected tothe slab end. In the optical waveguides shown in FIGS. 13A and 13B,although one kind of material is used as a material of the boundarysurface region BS, a plurality of kinds of materials may be used incombination.

The phase grating GP shown in FIG. 12D is provided with the refractiveindex difference region 12 and an island-shaped region 15. Therefractive index difference region 12 is provided with regions having alarge width and regions having a small width in the directionsubstantially vertical to the light propagation direction, and isintegral across the entire phase grating GP. The regions with a largewidth are arranged in the slab waveguide 1 at a distance in thedirection substantially vertical to the light propagation direction andhave a refractive index different from the refractive index of theregion shown by diagonal lines. Each of the regions with a small widthis held between the region shown by diagonal lines and the island-shapedregion 15, has a refractive index equal to the refractive index of theregions with a large width, and connects the regions with a large widthadjacent thereto.

The refractive index of the refractive index difference region 12 may belarger or smaller than the refractive index of the portion shown bydiagonal lines. The region with a large refractive index and the regionwith a small refractive index are alternately arranged in the directionsubstantially vertical to the light propagation direction, whereby thephase grating GP can be easily formed.

In the optical waveguide shown in FIG. 12D, the light propagationdirection width of the island-shaped region 15 is set to L1 shown inFIGS. 6A to 6C. In the optical waveguide shown in FIG. 12D, although theisland-shaped region 15 has a rectangular shape, the island-shapedregion 15 may have any shape. Also in the optical waveguide shown inFIG. 12D, as in the optical waveguide shown in FIGS. 13A and 13B, theboundary surface region BS may be formed on a boundary surface betweenregions with different refractive indices.

In the optical waveguide shown in FIGS. 12A, 12B, 12C and 12D, althoughthe convex regions 13 and 14 or the island-shaped region 15 are formedon an extension line of the arrayed waveguide 2, the convex regions 13and 14 or the island-shaped region 15 may be formed on an extension linebetween the arrayed waveguides 2 adjacent to each other in the directionsubstantially vertical to the light propagation direction. As in theoptical waveguide shown in FIGS. 14A, 14B and 14C, as long as a phasedifference can be given to light, the convex regions 13 and 14 or theisland-shaped region 15 may be formed on the extension line of thearrayed waveguide 2 and the extension line between the arrayedwaveguides 2 adjacent to each other in the direction substantiallyvertical to the light propagation direction.

In the optical waveguide shown in FIG. 14A, the convex regions 13 and 14are formed on the extension line of the arrayed waveguide 2, and theisland-shaped region 15 is formed on the extension line between thearrayed waveguides 2 adjacent to each other in the directionsubstantially vertical to the light propagation direction. The convexregion 13 and the island-shaped region 15 adjacent to each other areconnected at the corners, and the convex region 14 and the island-shapedregion 15 adjacent to each other are connected at the corners.

In the optical waveguide shown in FIG. 14B, the convex regions 13 and 14are formed on the extension line of the arrayed waveguide 2, anisland-shaped region 15-1 is formed on the extension line between thearrayed waveguides 2 adjacent to each other in the directionsubstantially vertical to the light propagation direction, and anisland-shaped region 15-2 is formed on the extension line of the arrayedwaveguide 2. The island-shaped regions 15-1 and 15-2 are arranged at adistance in the direction substantially vertical to the lightpropagation direction, and the island-shaped regions 15-1 and 15-2 thusarranged are alternately arranged in the direction substantiallyparallel to the light propagation direction. The convex region 13 andthe island-shaped region 15-1 adjacent to each other are connected atthe corners, the convex region 14 and the island-shaped region 15-1adjacent to each other are connected at the corners, and theisland-shaped regions 15-1 and 15-2 adjacent to each other are connectedat the corners.

In the optical waveguide shown in FIG. 14C, the convex regions 13 and 14are formed on the extension line of the arrayed waveguide 2, and theisland-shaped region 15 is formed on the extension line between thearrayed waveguides 2 adjacent to each other in the directionsubstantially vertical to the light propagation direction. The convexregion 13 and the island-shaped region 15 adjacent to each other are notconnected, and the convex region 14 and the island-shaped region 15adjacent to each other are not connected.

When the amplitude grating GA is formed instead of the phase grating GP,the portion becoming the refractive index difference region 11 of FIG. 9is filled with a light-shielding material which is excellent in lightabsorption. As the light-shielding material, a silicone resin, an epoxyresin, or the like mixed with carbon black and metal fine particles isused.

Embodiment 4

In the Embodiment 4, an arrayed waveguide grating provided with theoptical waveguide described in the Embodiments 1 to 3 will be described.In the arrayed waveguide grating, one or more first input/outputwaveguide(s), a first slab waveguide, a plurality of arrayed waveguides,a second slab waveguide, and one or more second input/outputwaveguide(s) are connected in this order. The first slab waveguide andthe plurality of arrayed waveguides constitute the optical waveguidedescribed in the Embodiments 1 to 3, serving as a slab waveguide 1 andan arrayed waveguide 2, respectively.

Although light with a plurality of wavelengths propagates in the firstslab waveguide, an arbitrary wavelength in the plurality of wavelengthsis selected as λ in FIGS. 1 and 2. The arbitrary wavelength is a centerwavelength in the plurality of wavelengths, for example. When thearbitrary wavelength is selected, the designing method described in theEmbodiment 2 and the manufacturing method described in the Embodiment 3are applied.

The grating may be disposed in not only the first slab waveguide butalso the second slab waveguide. The grating may be disposed in only thefirst slab waveguide, and the transition region of the Patent Documents1 to 4 or the slope portion of the Patent Document 5 may be disposed inthe second slab waveguide.

Embodiment 5

In an arrayed waveguide grating, when light input from a center port isdemultiplexed, loss imbalance occurs between output ports. This isbecause phase error dependent on wavelength is given to light reachingthe output port; and the farther away from an output side center port,the larger the phase error. When lights are multiplexed according to thereciprocity of light, intensity imbalance due to wavelength occurs. Whena phase grating is provided, the phase grating is designed by onewavelength; therefore, the phase error due to deviation from designwavelength occurs, also resulting in imbalance. In the Embodiment 5,there will be described the fact that, in the case where the arrayedwaveguide grating described in the Embodiment 4 is used as ademultiplexer, a light propagation direction width L2 of an interferenceregion IF provided in an output side slab waveguide is adjusted, wherebythe loss uniformity between output channels can be improved. FIGS. 15 to17 are views showing calculation results of insertion loss of thearrayed waveguide grating with various light propagation directionwidths L2 of the interference region IF, wherein a phase grating GP1 isused, and d=10.0 μm, λ=1.55 μm, and n=1.45.

FIG. 15 is a view showing loss distributions between the output channelsdepending on various L2. The output center port is represented as “0”,and in L=45 μm corresponding to m˜1 with the least loss, normalizationis performed with reference to loss of a center channel. In L=45 μmcorresponding to m˜1, although loss of the output channel near thecenter is reduced, the closer to both edges of the output channel, thelarger the loss. This is because the farther away from the center port,the larger the phase error. When L2 is changed to shift from the stateof the orders of m˜1, and, thus, to place in a defocusing state,although the loss of the output channel near the center significantlyincreases, the loss is less affected, and the loss distribution becomesflat, since the phase error originally occurs at the edges.

FIG. 16 is a view showing a relationship between L2 and minimum loss in33 output channels, i.e. −16 to 16 channels, described in FIG. 15, andFIG. 17 is a view showing a relationship between L2 and loss variationbetween output channels. When the 33 output channels, i.e. −16 to 16channels, are used, it can be shown that the loss variation is reducedthe most when L2=60 μm.

As described above, the loss and the loss variation are changed bychanging L2, therefore, by optimizing L2, the optical waveguide can bedesigned depending on the number of the output channels and a purpose ofuse of the optical waveguide. Although there has been described thephase grating provided in the output side slab waveguide when used as ademultiplexer in the present embodiments, the same applies to the phasegrating provided in an input side slab waveguide when used as amultiplexer. If the phase gratings are provided in the both slabwaveguides, when used as a multiplexer or a demultiplexer, the lossvariation can be reduced even if light is input from either of the slabwaveguides.

EXPLANATION OF REFERENCE SIGNS

-   1: Slab waveguide-   2: Arrayed waveguide-   11, 12: Refractive index difference region-   13, 14: Convex region-   15: Island-shaped region-   GP: Phase grating-   GA: Amplitude grating-   SP, SA: Self-image-   ED: End region-   IF: Interference region-   BS: Boundary surface region

What is claimed is:
 1. An arrayed waveguide grating comprising: one ormore first input/output waveguide(s); a first slab waveguide connectedto an end of the one or more first input/output waveguide(s); an arrayedwaveguide connected to an end of the first slab waveguide on an oppositeside of the one or more first input/output waveguide(s); a second slabwaveguide connected to an end of the arrayed waveguide on an oppositeside of the first slab waveguide; one or more second input/outputwaveguide(s) connected to an end of the second slab waveguide on anopposite side of the arrayed waveguide; and a phase grating formed inthe first slab waveguide at a distance from the end of the first slabwaveguide, and wherein an end of the arrayed waveguide is connected to aposition where a constructive interference portion of a self-image ofthe phase grating is formed, wherein the phase grating comprises:refractive index identity regions which have a refractive indexidentical with the refractive index of the regions in the first slabwaveguide other than the phase grating; and refractive index differenceregions which have a refractive index different from the refractiveindex of the regions in the first slab waveguide other than the phasegrating, wherein the refractive index identity regions comprise at leastone of the following: convex regions which protrude from an incidentregion of the phase prating and/or an interference region of the phasegrating, and which are disposed at a distance in a directionsubstantially vertical to a light propagation direction; andisland-shaped regions which are separated from the incident region ofthe phase grating and the interference region of the phase grating, andwhich are disposed at a distance in the direction substantially verticalto the light propagation direction, wherein the refractive indexidentity regions and the refractive index difference regions aredisposed alternatively in the direction substantially vertical to thelight propagation direction.
 2. The arrayed waveguide grating accordingto claim 1, wherein the refractive index difference regions are integralwith each other across the entire phase grating.
 3. The arrayedwaveguide grating according to claim 1, wherein a phase difference givento incident light by the phase grating is approximately 90 degrees. 4.The arrayed waveguide grating according to claim 1, wherein a phasedifference given to incident light by the phase grating is approximately180 degrees.
 5. The arrayed waveguide grating according to claim 1,wherein a plurality of boundary surface regions whose surface extend ina direction different from directions substantially parallel andsubstantially vertical to the light propagation direction are formed onboundary surfaces between regions with different refractive indices. 6.The arrayed waveguide grating according to claim 3, wherein a lightpropagation width of the interference region of the phase grating ismd²/(2(λ/n)), where m is an odd integer, d is a period of the phasegrating, λ is wavelength of light in vacuum, and n is a refractive indexof the interference region.
 7. The arrayed waveguide grating accordingto claim 4, wherein a light propagation width of the interference regionof the phase grating is md²/(8(λ/n)), where m is an odd integer, d is aperiod of the phase grating, λ is wavelength of light in vacuum, and nis a refractive index of the interference region.
 8. An opticalwaveguide comprising: a first slab waveguide in which a phase grating isformed therein at a distance from an end thereof; and an end of anarrayed waveguide is connected to a position where a constructiveinterference portion of a self-image of the phase grating is formed,wherein the phase grating comprises: refractive index identity regionswhich have a refractive index identical with the refractive index of theregions in the first slab waveguide other than the phase grating; andrefractive index difference regions which have a refractive indexdifferent from the refractive index of the regions in the first slabwaveguide other than the phase grating, wherein the refractive indexidentity regions comprise at least one of the following: convex regionswhich protrude from an incident region of the phase prating and/or aninterference region of the phase grating, and which are disposed at adistance in a direction substantially vertical to a light propagationdirection; and island-shaped regions which are separated from theincident region of the phase grating and the interference region of thephase grating, and which are disposed at a distance in the directionsubstantially vertical to the light propagation direction, wherein therefractive index identity regions and the refractive index differenceregions are disposed alternatively in the direction substantiallyvertical to the light propagation direction.
 9. The optical waveguideaccording to claim 8, wherein the refractive index difference regionsare integral with each other across the entire phase grating.
 10. Theoptical waveguide according to claim 8, wherein a phase difference givento incident light by the phase grating is approximately 90 degrees. 11.The optical waveguide according to claim 8, wherein a phase differencegiven to incident light by the phase grating is approximately 180degrees.
 12. The optical waveguide according to claim 10, wherein alight propagation width of the interference region of the phase gratingis md²/(2(λ/n)), where m is an odd integer, d is a period of the phasegrating, λ is wavelength of light in vacuum, and n is a refractive indexof the interference region.
 13. The optical waveguide according to claim11, wherein a light propagation width of the interference region of thephase grating is md²/(8(λ/n)), where m is an odd integer, d is a periodof the phase grating, λ is wavelength of light in vacuum, and n is arefractive index of the interference region.
 14. The optical waveguideaccording to claim 8, wherein a plurality of boundary surface regionswhose surface extend in a direction different from directionssubstantially parallel and substantially vertical to the lightpropagation direction are formed on boundary surfaces between regionswith different refractive indices.